We HIGHLY recommend you stop by Orange Blossom Bakery and get an Apple Ugly. Fair warning, they are only open 6:30 - 11 am (or they sell out) but are totally worth getting up early. The Apple Uglies are heavy and can easily be shared - but be prepared to fight for the last bite! We've also had their breakfast sandwiches and liked them if you need some protein.
The Outer Banks have the largest waves on the East Coast because it is situated to receive swells from multiple direction, making it a great spot for surfers. We generally also find the beaches in this area to be fairly isolated and great for looking for shells or just working on your tan and reading.